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Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory

Author

Listed:
  • Yusheng Zhou

    (Guizhou University)

  • Zaihua Wang

    (Nanjing University of Aeronautics and Astronautics)

  • Kwok-wai Chung

    (City University of Hong Kong)

Abstract

This paper presents a control design method for implementing planar turning motion of a two-wheeled inverted pendulum with an input delay. The control task requires that the inverted pendulum is kept stabilized during the whole turning motion process along a pre-settled curve. Firstly, by using the theory of planar curve, key observations about the motion law of the two-wheeled mobile chassis are made and they are used to set up a dynamical trajectory tracking target. Then, by adjusting the parameters in the tracking target and the weights in the quadratic performance criterion, the optimal integral sliding mode controller based on a linear quadratic regulator is designed for keeping the vehicle body stabilized and tracking a circular path for the two-wheeled inverted pendulum. An illustrative example is given to demonstrate the validity of the theory with numerical simulation.

Suggested Citation

  • Yusheng Zhou & Zaihua Wang & Kwok-wai Chung, 2019. "Turning Motion Control Design of a Two-Wheeled Inverted Pendulum Using Curvature Tracking and Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 181(2), pages 634-652, May.
    • Handle: RePEc:spr:joptap:v:181:y:2019:i:2:d:10.1007_s10957-019-01472-4
    DOI: 10.1007/s10957-019-01472-4
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    References listed on IDEAS

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    1. Ido Halperin & Grigory Agranovich & Yuri Ribakov, 2017. "Optimal Control of a Constrained Bilinear Dynamic System," Journal of Optimization Theory and Applications, Springer, vol. 174(3), pages 803-817, September.
    2. Jiaxing Che & Michael Santone & Chengyu Cao, 2015. "Adaptive Control for Systems with Output Constraints Using an Online Optimization Method," Journal of Optimization Theory and Applications, Springer, vol. 165(2), pages 480-506, May.
    3. Yusheng Zhou & Zaihua Wang, 2016. "Motion Controller Design of Wheeled Inverted Pendulum with an Input Delay Via Optimal Control Theory," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 625-645, February.
    4. Rongjie Liu & Shihua Li, 2014. "Suboptimal Integral Sliding Mode Controller Design for a Class of Affine Systems," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 877-904, June.
    5. Sergey A. Reshmin & Felix L. Chernousko, 2014. "Properties of the Time-Optimal Feedback Control for a Pendulum-Like System," Journal of Optimization Theory and Applications, Springer, vol. 163(1), pages 230-252, October.
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    Cited by:

    1. Ouxue Li & Yusheng Zhou, 2021. "Precise Trajectory Tracking Control of Ship Towing Systems via a Dynamical Tracking Target," Mathematics, MDPI, vol. 9(9), pages 1-18, April.

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